I cut my very large produce into chunks and put it in the large suet cake cages that hang in the run. My girls don't get to free range but a few hours every day (longer on certain days)--so, I thought this would be entertaining to them them...they seem to really enjoy their 'buffet' baskets and it's the first thing they check when I open the coop each morning...
When I chop things up small, there aren't any left overs. When I throw hole things or big junks in there, it's there for days and I have to toss it over the fence.
So to prevent waste from my "picky" birds, I cook anything hard, and I cut everything up small. They REALLY like carrot peelings, but I chop those up into manageable pieces. They also enjoy whatever mush comes out of the juicer, and pepper seeds (from green/red/yellow peppers, not hot ones!)
If I give them a bowl of chopped up Bantam sized bits, it's gone in a day. If I give them whole things, they might not even touch it. So the only whole things I give them is sweet corn, they seem to enjoy pecking that.
Raw potatos and potato peelings can be toxic in too large of amount. They contain a chemical that is destroyed by cooking or aging. Too many green peels will kill mammals. I do not feed anything potato peels or raw potatos for that reason. Potato peels are one of the few food waste items I throw away. This is pretty much only true for the large baking potato type. Sweet potatos and I believe the "waxy potatos" do not have that risk.
The reasoning behind halving the grapes is so that they don't get stuck in the animals' throat. Grapes don't melt so if they get stuck the animal chokes on it. I heard that first on rabbit lists.